A person with a head injury during the time of the Prophet PBUH was asked to wash his head for Wudu, the prophet PBUH later said to the people who told him so "They killed him, Allah may kill them", wasn't it a cure to just ask.

My personal take from the Hadith is that nothing is set in stone and if there is a way something can happen to make things easier for you, you should do as long as you have the correct interruption.

Personally, I think if you need to pray Asr at a certain time and it is convenient for you, go ahead. Allah meant this deen to be easy and not complicated. Sometimes I pray Friday in one Masjid 1 hour before Zhur and sometimes in another Masjid 2 hours after. It is all on what is best to you.

Yahya related to me from Malik from Yazid ibn Ziyad that Abdullah ibn
Rafi, the mawla of Umm Salama, the wife of the Prophet, may Allah
bless him and grant him peace, asked Abu Hurayra about the time of the
prayer. Abu Hurayra said, "Let me tell you. Pray dhuhr when the length
of your shadow matches your height, asr when your shadow is twice your
height, maghrib when the sun has set, isha in the first third of the
night, and subh in the very first light of dawn," i.e. when the dawn
has definitely come.

But consider that the differences could sometimes come from mistakes in calculation or extreme carefulness. For example in the internet you can find many different calculation methods and many prayer times for the same prayer sometimes with diffrences of an hour or more!